Tree Thinking

April Wright
08.09.2018

Good Morning!

  • What is a tree?
  • How is a tree built?
  • What are phylogenetic data?

What do we do with a phylogeny?

  • Determine the timing of trait evolution

Skink tree from Wright et al. 2015

What do we do with a phylogeny?

-Tell homology from convergence

Dolphin, Alex Vasenin via WikiMedia Dolphin

What do we do with a phylogeny?

-Trace the origins of structures

Ask a Biologist

What do we do with a phylogeny?

-Taxonomy

  • Hennig, 1950 Grundzüge einer Theorie der Phylogenetischen Systematik
    • Taxonomy should be logically consistent with the tree for the group

What do we do with a phylogeny?

-Taxonomy

  • Hennig, 1950 Grundzüge einer Theorie der Phylogenetischen Systematik
    • Taxonomy should be logically consistent with the tree for the group
  • Sneath & Sokal, 1963, 1973
    • Using distance matrices to cluster based on phenetic similarity

Tree Terms: Tip

library(phytools)
tree <- pbtree(n = 5)
plot(tree, cex = 3.5, no.margin = TRUE, edge.width = 1.5)

plot of chunk unnamed-chunk-1 Tip: What we are putting on the tree. May be species, individuals, or higher-order taxa. May be called terminal node, leaf, one degree node.

Tree Terms: Tip

library(phytools)
tree <- pbtree(n = 5)
plot(tree, cex = 3.5, no.margin = TRUE, edge.width = 1.5)

plot of chunk unnamed-chunk-2 Branch: What connects the tip to the tree. Can have a variety of units, which we will discuss over the next few days. May be called edge.

Tree Terms: Node

library(phytools)
tree <- pbtree(n = 5)
plot(tree, cex = 3.5, no.margin = TRUE, edge.width = 1.5)
nodelabels()

plot of chunk unnamed-chunk-3 Node: Where nodes meet, implying a most recent common ancestor. May be called vertex, or three-degree node.

Tree Terms

plot(tree, cex = 3.5, no.margin = TRUE, edge.width = 1.5, direction = "downwards")

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Tree Terms

plot(tree, cex = 3.5, no.margin = TRUE, edge.width = 1.5, type="fan")

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Tree Terms: Rotation - reflecting taxa at a node

plot(tree, cex = 3.5, no.margin = TRUE, edge.width = 1.5)
nodelabels(cex = 3.5)

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#rotateNodes(tree, c(7, 8))
#plot(tree, cex = 3.5, no.margin = TRUE, edge.width = 1.5)

Tree Terms: Monophyletic - an ancestor and all its descendents

is.monophyletic(tree, c("t1", "t2"), plot = TRUE, edge.width = 1.5, cex = 3.5, no.margin = TRUE)

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[1] FALSE

Tree Terms: Rooting

# reroot(tree, node.number)
plot(tree, cex = 3.5, no.margin = TRUE, edge.width = 1.5)

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Ingroup: Taxa of interest

Outgroup: Taxon closely related used to root the tree

Tree Terms: Rooting

unroot_tree <- unroot(tree)
plot(unroot_tree, cex = 3.5, no.margin = TRUE, edge.width = 1.5)

plot of chunk unnamed-chunk-9

How is a tree built?

  • Many ways. We will focus on three:
    • Maximum parsimony
    • Maximum likelihood
    • Bayesian inference

Phylogenetic Data

library(alignfigR)
char_data <- read_alignment("data/bears_fasta.fa")
char_data[1:3]

$Agriarctos_spp
 [1] "?" "0" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "0"
[18] "0" "0" "1" "1" "1" "1" "0" "0" "1" "?" "1" "1" "?" "0" "1" "1" "1"
[35] "1" "0" "1" "1" "0" "?" "?" "0" "1" "1" "1" "0" "?" "?" "?" "?" "?"
[52] "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?"

$Ailurarctos_lufengensis
 [1] "?" "0" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?"
[18] "0" "0" "1" "1" "1" "1" "0" "1" "1" "?" "1" "1" "?" "0" "?" "?" "?"
[35] "?" "0" "1" "1" "1" "?" "0" "0" "1" "1" "1" "0" "1" "0" "1" "1" "0"
[52] "1" "1" "?" "?" "?" "?" "?" "?" "?" "?" "?"

$Ailuropoda_melanoleuca
 [1] "1" "0" "1" "1" "1" "1" "0" "1" "1" "0" "1" "0" "0" "1" "0" "0" "0"
[18] "0" "0" "1" "1" "1" "1" "0" "1" "0" "1" "1" "1" "0" "0" "1" "0" "1"
[35] "0" "0" "1" "1" "0" "0" "0" "0" "1" "1" "1" "0" "1" "0" "0" "1" "0"
[52] "1" "1" "0" "0" "0" "1" "0" "0" "0" "1" "0"

Phylogenetic Data

library(alignfigR)
char_data <- read_alignment("data/bears_fasta.fa")
char_data[1:3]

$Agriarctos_spp
 [1] "?" "0" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "0"
[18] "0" "0" "1" "1" "1" "1" "0" "0" "1" "?" "1" "1" "?" "0" "1" "1" "1"
[35] "1" "0" "1" "1" "0" "?" "?" "0" "1" "1" "1" "0" "?" "?" "?" "?" "?"
[52] "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?"

$Ailurarctos_lufengensis
 [1] "?" "0" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?"
[18] "0" "0" "1" "1" "1" "1" "0" "1" "1" "?" "1" "1" "?" "0" "?" "?" "?"
[35] "?" "0" "1" "1" "1" "?" "0" "0" "1" "1" "1" "0" "1" "0" "1" "1" "0"
[52] "1" "1" "?" "?" "?" "?" "?" "?" "?" "?" "?"

$Ailuropoda_melanoleuca
 [1] "1" "0" "1" "1" "1" "1" "0" "1" "1" "0" "1" "0" "0" "1" "0" "0" "0"
[18] "0" "0" "1" "1" "1" "1" "0" "1" "0" "1" "1" "1" "0" "0" "1" "0" "1"
[35] "0" "0" "1" "1" "0" "0" "0" "0" "1" "1" "1" "0" "1" "0" "0" "1" "0"
[52] "1" "1" "0" "0" "0" "1" "0" "0" "0" "1" "0"

These data are binary

Phylogenetic Data

library(alignfigR)
char_data <- read_alignment("data/bears_fasta.fa")
char_data[1:3]

$Agriarctos_spp
 [1] "?" "0" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "0"
[18] "0" "0" "1" "1" "1" "1" "0" "0" "1" "?" "1" "1" "?" "0" "1" "1" "1"
[35] "1" "0" "1" "1" "0" "?" "?" "0" "1" "1" "1" "0" "?" "?" "?" "?" "?"
[52] "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?"

$Ailurarctos_lufengensis
 [1] "?" "0" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?" "?"
[18] "0" "0" "1" "1" "1" "1" "0" "1" "1" "?" "1" "1" "?" "0" "?" "?" "?"
[35] "?" "0" "1" "1" "1" "?" "0" "0" "1" "1" "1" "0" "1" "0" "1" "1" "0"
[52] "1" "1" "?" "?" "?" "?" "?" "?" "?" "?" "?"

$Ailuropoda_melanoleuca
 [1] "1" "0" "1" "1" "1" "1" "0" "1" "1" "0" "1" "0" "0" "1" "0" "0" "0"
[18] "0" "0" "1" "1" "1" "1" "0" "1" "0" "1" "1" "1" "0" "0" "1" "0" "1"
[35] "0" "0" "1" "1" "0" "0" "0" "0" "1" "1" "1" "0" "1" "0" "0" "1" "0"
[52] "1" "1" "0" "0" "0" "1" "0" "0" "0" "1" "0"

Always arranged with rows being taxa and columns corresponding to a character - “matrix” structure

Phylogenetic Data

Example character from Brady:

  1. Worker, queen, and male. Specialized, stout setae on anterior margin of clypeus: (0) absent; (1) present. The presence of these specialized setae is a putative synapomorphy of Amblyoponinae (Ward, 1994), including Amblyopone and Onychomyrmex.

Phylogenetic Data

  • How do we know we have a truly discrete state?

Phylogenetic Data

How do we know we've captured the relevant character axes?

Ask a biologist, Mike Hagelberg

Phylogenetic Data

library(ggplot2)
colors <- c("blue", "purple","white")
plot_alignment(char_data, colors, taxon_labels = TRUE) + theme(text = element_text(size=40))

plot of chunk unnamed-chunk-13

Phylogenetic Data

library(ggplot2)
colors <- c("blue", "purple","white")
plot_alignment(char_data, colors, taxon_labels = TRUE) + theme(text = element_text(size=40))

plot of chunk unnamed-chunk-14 How do we go from this to a tree?

Parsimony

  • Not only applied in phylogenetics
  • The simplest explanation for the observed data is the best

Parsimony

  • Maximum parsimony: the tree that minimizes the number of “steps”, or changes, on a tree is to be preferred
  • Let's turn to the board for a minute: Parsimony informative, invariant, and parsimony non-informative variation

??? Have them start installs on the next page while we do this.

treesiftr

library(treesiftr)
aln_path <- "data/bears_fasta.fa"
bears <- read_alignment(aln_path)
tree <- read.tree("data/starting_tree.tre")

sample_df <- generate_sliding(bears, start_char = 1, stop_char = 5, steps = 1)
print(sample_df)

  starting_val stop_val step_val
1            1        2        1
2            2        3        1
3            3        4        1
4            4        5        1
5            5        6        1

treesiftr

library(phangorn)
library(ggtree)
output_vector <- generate_tree_vis(sample_df = sample_df, alignment =                                        aln_path,tree = tree, phy_mat = bears,                                    pscore = TRUE)

Final p-score 2 after  0 nni operations 
Final p-score 2 after  0 nni operations 
Final p-score 2 after  0 nni operations 
Final p-score 2 after  1 nni operations 
Final p-score 2 after  1 nni operations

treesiftr

output_vector #sample output - you will get more than this when you run in your console

[[1]]

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[[2]]

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[[3]]

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[[4]]

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[[5]]

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??? Do a couple trees on the board, including the pruning algorithm. Then allow them to play.

Parsimony: Many trees for one character and 4 taxa

Parsimony Trees

??? This is one character. Imagine many - enumeration is not possible.Also note that several trees have the same “best” tree

Parsimony: How do we find the most parsimonious tree?

  • We're going to take an exercise break and play with PAUP

PAUP

execute data/bears_morphology.nex
  • NOTE: PAUP allows tab-completion
  • Open the bears_morphology file in a text editor. Now:

PAUP: A couple important commands

cstatus
tstatus
showmatrix
showdist
log file="mylogfile"
  • Try each of these - what information do they give you?

PAUP: Building a tree

alltrees

What happened here?

Parsimony: Enumeration is not possible for more than 12 taxa

Parsimony Trees

??? This is one character. Imagine many - enumeration is not possible.Also note that several trees have the same “best” tree

PAUP: Heuristic Searches

Heuristic - use of shortcuts to reduce the number of trees we need to search

hsearch
  • What is the name of the heuristic that was used?
  • How was the initial tree discovered?
  • How many trees were searched?
  • How many “best” trees were there, and what is their score?

PAUP: Heuristic Searches

Heuristic - use of shortcuts to reduce the number of trees we need to search

hsearch swap = nni
  • How many trees were examined with this algorithm? Why is this number so much smaller?
  • How many “best” trees were found, and what is their score?

PAUP: Heuristic Searches

Heuristic - use of shortcuts to reduce the number of trees we need to search

hsearch swap = spr
  • How many trees were examined with this algorithm?
  • How many “best” trees were found, and what is their score?
  • When would we expect searching algorithm to matter strongly?

PAUP: Exporting parsimony trees

savetrees from=1 to=1 file=results/tree1.tre;
savetrees from=2 to=2 file=results/tree2.tre;
savetrees from=3 to=3 file=results/tree3.tre;

PAUP: Reading in parsimony trees

library(ape)
tree1 <- read.nexus("results/tree1.tre")
tree2 <- read.nexus("results/tree2.tre")
tree3 <- read.nexus("results/tree3.tre")

PAUP: What do we do with multiple "best" trees?

Parsimony Trees

??? This is one character. Imagine many - enumeration is not possible.Also note that several trees have the same “best” tree

PAUP: What do we do with multiple "best" trees?

  • Typically: Build a consensus tree
  contree all / treefile=Results/contree.tre;
  help contree
  • Please look at:
    • Semistrict
    • Majority rule
    • Adams

How do we assess confidence in a tree?

  • The bootstrap
char_mat <- phangorn::phyDat(char_data, levels = c(0, 1, "?"), type = "USER")
samples <- sample(1:62, 62, replace = TRUE)
new_mat <- subset(char_mat, select=samples)
samples

 [1]  6  8 22 13 11 45 16  6 43 33 43 32 47 60 59 25 14 33  2 18 22 54 25
[24] 12 21 20 56 43  3 12 10 34 57 25  9 18 22 20 12 53  1 12 20 44 40 22
[47] 18 12  6 21  3  4 54 55 25 59 48 15 38 25  6 42

How do we assess confidence in a tree?

  • The bootstrap samples characters with replacement
char_mat <- phangorn::phyDat(char_data, levels = c(0, 1, "?"), type = "USER")
list_of_mats <- list()
for (i in 1:100){
samples <- sample(1:62, 62, replace = TRUE)
new_mat <- subset(char_mat, select=samples)
list_of_mats[[i]] <- new_mat
}

Generates a tree from each matrix

The bootstrap

plot(tree1)

plot of chunk unnamed-chunk-29

PAUP: The bootstrap

bootstrap nreps=100 search=heuristic /addseq=random;
savetrees from=1 to=1 savebootp=nodelabels file=results/bootstrap.tre;

b_tre <- read.nexus("results/bootstrap.tre")
plot(b_tre)
nodelabels(b_tre$nodelabels)

plot of chunk unnamed-chunk-31

PAUP: The bootstrap

bootstrap nreps=100 search=heuristic /addseq=random;
savetrees from=1 to=1 savebootp=nodelabels file=results/bootstrap.tre;

b_tre <- read.nexus("results/bootstrap.tre")
plot(b_tre)
nodelabels(b_tre$node.label)

plot of chunk unnamed-chunk-33 “b_tre$nodelabels” what is this construction?

PAUP: The jacknife

Samples without replacement

jackknife nreps=100 search=heuristic /addseq=random;
savetrees from=1 to=1 savebootp=nodelabels file=results/jackknife.tre;

j_tre <- read.nexus("results/jackknife.tre")
plot(j_tre)
nodelabels(j_tre$node.label)

plot of chunk unnamed-chunk-35

Parsimony: Some of these trees imply homoplasy

Parsimony Trees

Is an answer that implies homoplasy ever the right one?

Parsimony: Different Step Matrices

  • Can make different character interchanges weigh more or less than others
  • For example, for character 1, it might be more likely to go from 0 to 1 than the reverse
  • Let's try this in PAUP

PAUP: Different Step Matrices

  • Open the bears_morphology file in a test editor. Scroll all the way to the bottom and paste in:
begin assumptions;
 usertype my_ctype stepmatrix=2
     0 1
 [0] . 1
 [1] 0 .

 ;
end;

PAUP: Different Step Matrices

  • In the PAUP executeable:
ctype my_ctype:1
hsearch

PAUP: Different Step Matrices

  • For those of you who are more familiar with likelihood and Bayesian analyses, what does this sound like?

  • We'll pick up this afternoon with Bayesian models